Three self-contained pages for 6D SU(4) gauge-Higgs unification on T^2/Z_2: the alpha-domain selection rule (Part III), a model calculator that takes a matter content and returns the Higgs (Parts IV-V), and an eta-meter that predicts what the boundary sign does in closed form and checks itself against the loop sum.

Schur functions at (1,-1,t,1/t): a closed form on the non-identity component of O(4) (Part IV).